My question is related to Gali chapter 8 (implemented by prof. Pfeifer) and the accurate way to read data from a file.
On github, you mentioned that all variables are in log-deviations from the steady state, but interest rate which is mean 0.
After reading the guide on observable variables, I proceeded the following way:
GDP (real quarterly volumes) → log(gdp) → get cylical component using univariate-HP filter
Read it from the file like: y_obs = yhat or y_obs = y_gap
Nominal interest rate (net annual percentages) → make it quarterly percentages ln(1 + rate/400) → get cyclical component using univariate-HP filter
Read it from the file like: i_obs = i
Inflation Rate (net quarterly percentages) → get cyclical component using univariate-HP filter
Read it from the file like: pi_obs = pi
Question 1: You mentioned that interest rate is mean 0, not in log-deviations from steady state. HP-filter also demeans the data and the cyclical component is mean 0. Nonetheless, shouldn’t there be a difference between the way you match output gap and how you match inflation / interest rate given one is mean 0 and the others in log-deviations?
Question 2: Given that all variables (but the abovementioned ones) are in log-deviations, is it appropriate to just detrend variables (log consumption per capita, log NX per capita) using univariate HP filter and consider the cyclical component as log-deviation from steady state and read it like c_obs = c & c_NX = NX plus some shock to avoid stochastic singularity?
Question 3: Is it ok to just take the log difference of variables such as nominal exchange and read it like er_obs = er - er(-1) + eps_er. I don’t understand why this is appropriate…I saw a lot of posts where people read variables like this, but I did not really understand why - er in the model is log deviation from steady state while er_obs is basically log difference of nominal rates → growth rate. How do these two match?